No not really as there are 3 castes in the gith and 2 of those aren't military, quite possible for a member of the lower caste to be a lv 1 fighter. You simply cannot be a level one character and have killed a beholder, end of story. Lae'zel is a good character and well voice acted and by far one of the more interesting of the bunch.
She cannot possibly "have never left the astral plane" because she is an adult, you don't age on the astral plane that's why creche are in the material realm. She has jeweled armor, the sign of being part of the miliary caste....I could go on. I am point out facts in D&D lore not couldawudashuda. If I see something out of place or doesn't make sense I am going to say so. Ok explain a 200 year old vampire rogue newb? Not conjecture either.
There is no "end of story" in DnD. Everything is up to the DM, even the rules as written. What is acceptable for a first level character at one table might not be at another. Personally if a player wanted to have been involved in a big fight against beholders I'd be fine with it as long as they didn't claim to 1v1 them. I've not gotten the specific beholder dialogue yet, but the way you phrased it sounded like she was fighting alongside others from her Creche, not soloing them all.
You misunderstood. She hasn't "never left the astral plane". She's never been TO the astral plane. She says she longs to one day visit it. This means she has not performed her rite of passage. She hasn't proven herself worthy of it yet, which is a big part of her character.